Comparison of the magnetic properties of ferromagnetic films and nanostructures

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Comparison of the magnetic properties of

ferromagnetic films and nanostructures

Dissertation

zur Erlangung des Doktorgrades

an der Fakultät für Mathematik, Informatik und Naturwissenschaften Fachbereich Physik

der Universität Hamburg

vorgelegt von

Stefan Freercks

Hamburg 2020

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Zusammensetzung der Prüfungskommission: Prof. Dr. Hans Peter Oepen Prof. Dr. Robert H. Blick Prof. Dr. Wolfgang Hansen Prof. Dr. Daniela Pfannkuche Prof. Dr. Dorota Koziej

Vorsitzender der Prüfungskommission: Prof. Dr. Wolfgang Hansen

Datum der Disputation: 17.11.2020

Vorsitzender des Fach-Promotionsausschusses PHYSIK: Prof. Dr. Günter H.W. Sigl

Leiter des Fachbereichs PHYSIK: Prof. Dr. Wolfgang Hansen

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Abstract

This thesis deals with the magnetic properties of ultrathin Pt/Co/Pt films and nanostructures. The films are sputtered under high vacuum conditions. The nanostructures are then fabricated from the films by using electron beam lithogra-phy and argon ion milling. Pt/Co/Pt multilayers posses an uniaxial anisotropy that is either in-plane or out-of-plane, depending on the thickness of the cobalt layer.

Pt/Co/Pt multilayer with an in-plane anisotropy are investigated and the tem-perature dependence of the magnetic anisotropy is measured. The Co thickness tCo is varied and the films are either sputtered on a SiO2 or Si3N4 substrates.

At tCo≤ 2 nm the anisotropy increases linearly with increasing temperature for

both substrates. For thicker films the anisotropy decreases. Interface and volume anisotropy have been determined. The interface anisotropy linearly increases with increasing temperature, while the volume anisotropy decreases. Since the conven-tional method to determine the volume and interface anisotropy assumes that the interfaces between Co and Pt are perfect, a model is proposed that takes alloying at the interfaces, caused by interdiffusion, into consideration. Due to the alloying, the saturation magnetisation is reduced with increasing temperature, resulting in an increase of the anisotropy. The effect on the volume anisotropy is negligible. However, the conventional approach of using sharp interfaces, overestimates the interface anisotropy.

For single magnetic nanostructures, the magnetisation behaviour has been in-vestigated. The three dimensional switching surface has been measured and a deviation from the uniaxial anisotropy model is found. It is known from previous simulations [1], that these deviation stem from a tilt between different anisotropy contributions, that is caused by the local grain structure.

While measuring the temperature dependence of the switching field in the blocked regime and the switching frequency in the superparamagnetic regime, a too high attempt frequency of the Néel-Arrhenius law is found. Since the temperature dependence of the anisotropy can explain such a behaviour, the latter is measured. The temperature dependence is inherited from the initial film possesses however, the wrong sign to correct the too high attempt frequency.

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Zusammenfassung

Diese Arbeit widmet sich den magnetischen Eigenschaften von ultradünnen mag-netische Filmen, sowie magmag-netischen Nanostrukturen. Die Filme werden im Ultrahochvakuum mittels Sputterdeposition hergestellt. Die Nanostrukturen wer-den mit Elektronenstrahllithographie und Ionenätzen aus wer-den Filmen erzeugt. Bei den untersuchten Proben handelt es sich um Pt/Co/Pt-Schichtsysteme. Dieses System zeichnet sich durch eine uniaxiale Anisotropie aus, welche abhängig von der Kobalt Schichtdicke aus der Filmebene heraus zeigt oder parallel zur Filmebene liegt. Es wurden temperaturabhängige Messungen der Anisotropie von Filmen durchgeführt für verschiedene Kobalt-Dicken und verschiedene Substrate. Die leichte Achse der Magnetisierung liegt in der Filmebene. Dabei konnte gezeigt werden, dass die Anisotropie mit steigender Temperatur linear ansteigt. Das Vorzeichen der Steigung ist abhängig von der Co-Dicke. Bemerkenswert ist die positive Steigung bei dünnen Co-Schichten. Weiterhin wurde die Temperaturab-hängigkeit der Grenzflächen- sowie der Volumenanisotropie bestimmt. Für die Ermittlung der Anisotropiekonstanten werden perfekte Grenzflächen angenommen. Es wird ein Model vorgestellt, welches den Einfluss einer Legierungsbildung an den Grenzflächen berücksichtigt. Es konnte gezeigt werden, dass die Legierungsbildung zu einer Reduzierung der Sättigungsmagnetisierung führt. Während der Einfluss auf die Volumenanisotropie vernachlässigbar ist, führt die Annahme scharfer Gren-zflächen zu einer Überschätzung der GrenGren-zflächenanisotropie.

Für eine einzelne Nanostruktur wurde die drei-dimensionale Schaltfläche gemessen. Diese weicht stark vom uniaxialen Anisotropiemodel ab. Frühere Simulationen von Staeck [1] haben gezeigt, dass dieses Verhalten auf die lokale Kornstruktur zurückzuführen ist. Die Verkippung der Körner, führt zu einer Verkippung der einzelnen Anisotropiebeiträge.

Die Temperaturabhängigkeit des Schaltfeldes sowie der Schaltfrequenz ergeben eine zu hohe Versuchsschaltfrequenz. Da dieses durch die Temperaturabhängigkeit der Anisotropie erklärt werden kann, wird letztere untersucht. Die Temperaturab-hängigkeit wird vom ursprünglichen magnetischen Film übertragen, besitzt aber das falsche Vorzeichen um die Abweichung der Versuchsschaltfrequenz zu erklären. Zusammenfassend zeigt diese Thesis, dass häufig vernachlässigte Eigenschaften, wie die Legierungsbildung an den Grenzflächen oder die lokale Kornstruktur, die

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1 Introduction

The unstoppable advance of the information age leads to an increasing demand of data storage capacity. Since the development of the first hard disk drive (HDD) in 1956 by IBM [2], magnetic recording has been utilised and constantly researched. The underlying concept of magnetic recording is the storage of data in magnetic domains of granular magnetic media. The bits are defined as the direction of the magnetisation in the domains. Early on, the increase of data storage was hindered by the read heads, that are needed to read out the data. The breakthrough came in 1988, when Fert [3] and Grünberg [4] discovered the giant magneto-resistance that has been first used in 1997.

The cornerstone of today’s storage media is the perpendicular magnetic anisotropy (PMA). Based on PMA, perpendicular magnetic recording (PMR) was first pro-posed by Iwasaki in 1977 [5]. In PMR the magnetisation points perpendicular to the medium unlike the previous used longitudinal recording, where it lies in the plane. Though much higher storage densities can be achieved, it took 28 years until the first hard disk drives utilising PMR hit the market in 2005.

The everlasting increase in storage density is hindered by the superparamagnetic limit [6,7]. Superparamagnetism describes a magnetic state in very small magnetic structures, like the grains used as storage units. At a certain temperature, sponta-neous magnetisation reversal will be induced by thermal activation, resulting in a loss of residual magnetisation . The structure behaves like a paramagnet, only with a much stronger magnetisation. The limit is given by :

KV kBT

= 25 (1.1)

K stands for the magnetic anisotropy, V describes the volume of the nanostructure, kB is the Boltzmann constant and T is the temperature. It is evident, that the

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units, because eventually the units become superparamagnetic. The problem can be solved by increasing the magnetic anisotropy. However, a higher anisotropy results in a need of stronger magnetic fields to write the data. Such strong mag-netic field can not be achieved by the commonly used write heads [6,8,9].

This dilemma lead to the development of energy-assisted magnetic recording. One method is the heat-assisted magnetic recording (HAMR) [10]. A laser locally heats the magnetic medium, which lowers the needed magnetic write field. An alterna-tive to HAMR is microwave assisted magnetic recording (MAMR) [11,12]. Here, a spin-torque oscillator creates an additional magnetic field. A higher anisotropy becomes possible, which allows to reduce the size of the granular storage units and thereby increasing the storage density. As of today, the newest road map by the company Western Digital, shows that neither HAMR nor MAMR HDDs are realised. Instead a new concept simply called energy-assist PMR (ePMR) will be utilised. HAMR and MAMR are not to be released before 2023 [13].

PMA remains an important research topic today, not only due to PMR but also because of the possible application in spin-transfer torque magneto-resistive random access memory (STT-MRAM) [14]. The technique has the advantage of being non-volatile, because the data is stored in magnetic storage elements. Due to the possible application in data storage media, materials possessing PMA were studied intensively. Gradman et al. fabricated ultra-thin NiFe films on Cu(111) by means of epitaxy and measured PMA as early as 1966 [15]. Starting in 1985, Carcia found PMA in sputtered Co/Pd multilayers [16]. In the following years, PMA was also proven in Co/Pt [17], Co/Au [18], Co/Ru [19] and Co/Ir [20] multilayers. In the group of Prof. Oepen, Co/Pt films have been thoroughly studied [21–27]. A characteristic of sputtered multilayers, is the emergence of intermixing zones due to interdiffusion, which results in the formation of an alloy at the interfaces. Usually the influence of the intermixing zones on the magnetic properties is neglected. However, it will be shown that some properties are af-fected.

Despite the long history of research, basic properties like the temperature de-pendence of the anisotropy K(T ) are sparsely investigated. The temperature dependence of the anisotropy is well understood in bulk Co, but for the case of ultrathin Co/Pt multilayers, which is needed to create perpendicular magnetic anisotropy, the behaviour is not well understood. First measurements in our group

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were made by Kobs [26]. This thesis continuous on this investigation.

To further increase the data storage capacity, concepts beyond the energy-assisted magnetic recording are needed. One such concept is bit patterned media (BPM) [28], where nanodots are used as storage units, instead of grains in a magnetic film. The nanodots are made by electron beam lithography and can be compactly arranged, to maximise the storage density. For BPM to work, the switching field distribution needs to be small, so that the bits can be written by the same field strength. To understand if that is possible, the measurement and understanding of single nanodots is desirable.

The magnetisation behaviour of single nanodots is investigated, by using nanosized Hall bar magnetometry. The nanodots are carved out of ultra-thin Co/Pt films by using electron beam lithography and argon ion milling. The emphasize of this thesis lies on the angular dependence of the switching field, as well as the temperature dependence of the anisotropy. Further works in this project were done by A. Neumann [29], C. Thönnißen [30], P. Staeck [1] and E.-S. Wilhelm [31]. Also, results are published in [32].

Chapter 2 discusses the theoretical background and chapter 3 describes the experimental basics. Chapter 4 deals with the temperature dependence of the anisotropy in ultra-thin films. In chapter 5 the magnetisation behaviour of single magnetic nanodots is investigated. Chapter 6 is the conclusion.

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2 Theoretical background

In this chapter the theoretical background will be be discussed, that is necessary to understand the experimental outcome of this thesis. The main emphasis is put on the magnetic anisotropy and the magnetic behaviour of single domain particles. For further details [33–36] are referenced.

2.1 Basics of magnetism

The fundamental equation to describe magnetism in solid materials is given by:

~

M = ¯χ ~H (2.1)

~

H is the magnetic field strength vector, ¯χ the magnetic susceptibility tensor and ~

M the magnetisation vector. The latter is defined as ~M = d ~_dVm, where ~m is the atomic magnetic moment and V is the volume of the solid. The susceptibility ¯χ can be understood as the response of the magnetisation to an external magnetic field. In a case of a linear relation between ~H and ~M , the susceptibility becomes a scalar χ. Depending on sign and magnitude of χ three different classes of magnetic material are defined.

The case −1 < χ < 0 is defined as diamagnetism, where ~M is aligned in the opposite direction of the external field ~H.

The case 0 < χ < 1 is defined as paramagnetism. The magnetic moments of the individual atoms are randomly oriented and there is no residual magnetisation. By applying an external magnetic field, the magnetic moments can be aligned in the direction of the magnetic field, resulting in a magnetisation. The magnetisation can be described by a Langevin equation.

The case χ 1 is defined as ferromagnetism. Due to the exchange interaction, the magnetic moments are parallel aligned and build a residual magnetisation, that

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exist even without an external magnetic field. To minimise the demagnetisation energy, the ferromagnet builds domains.

2.2 Magnetic energy terms

To describe the magnetic energy EMag three different contributions are considered.

These are the exchange energy EExc, the magnetostatic energy EM−S, the magnetic

anisotropy energy EAni.

EMag = EExc+ EM−S+ EAni (2.2)

Exchange energy

The exchange interaction describes a quantum mechanical effect, that stems from the interplay of the spin dependent part of the Coulomb interaction and the Pauli principle. It couples neighbouring spins in a manner, that a parallel alignment is favoured. Because of the Pauli principle, the wave function of electrons is anti-symmetric regarding the permutation of two particles. The Hamiltonian HExc

is defined as: HExc = −2 X i<j JijS~iS~j (2.3) ~

Si and ~Sj are the spin functions of the neighbouring electrons i and j.

Magnetostatic energy

The magnetostatic energy has two contributions: First the Zeeman energy that describes the energy that is induced from an external magnetic field on a ferro-magnet and second the deferro-magnetisation energy, which stems from the external stray field that is created in a ferromagnet.

Zeeman energy

The Zeeman energy is given by:

EZeeman= −µ0

Z

V

~

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2.2 Magnetic energy terms

µ0 is the vacuum permeability given by 4π 10−7H/m. When the magnetic field

and the magnetisation are homogeneous, therefore independent of V , the formula is simplified by using the vector product:

EZeeman= −µ0V MSH cos(θ) (2.5)

MS is the saturation magnetisation and θ is the angle between ~M and ~H.

Demagnetisation energy

The demagnetisation energy is the result of the stray field of a ferromagnet. It is a result of the Maxwell equation div ~B = µ0div( ~M + ~HD) = 0, which is equivalent

to div ~M = −div ~H. The demagnetisation energy is then given by:

EDemag = − 1 2µ0 Z V ~ M · ~HDdV (2.6)

The demagnetisation energy is easy to calculate for a ellipsoid, where the magnetic field is homogeneous. This can also be approximated for a thin film, which is a limiting case of the ellipsoid. The magnetic field is given by ~HD = ¯ND· ~M. ¯ND is

the demagnetisation tensor, that depends on the shape of the sample. In the case of rotational symmetry of the ellipsoid the demagnetisation energy is given by:

EDemag= − 1 2µ0M 2 SV (Nk sin 2_{(θ) + N} ⊥ cos2(θ)) (2.7)

Here, θ is the angle between the magnetisation and the rotational axis and Nk

and N⊥ are the parallel and perpendicular contributions of the demagnetisation

tensor.

The demagnetisation energy depends on the direction of the magnetisation. In a thin film this is described by:

EDemag = − 1 2µ0M 2 SV cos 2_(θ) _(2.8)

θ is the angle between magnetisation and film plane. The demagnetisation energy is at a maximum for θ = 90◦ and at minimum for θ = 0◦, which means the magnetisation is favoured to lie in the film plane. The difference in energy density is called shape anisotropy Kshape = E(θ=0

◦_)−E(θ=90◦₎

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Shape anisotropy

The shape anisotropy of a magnetic film lies parallel to the film plane and is given by: Kshape,film = − 1 2µ0M 2 S (2.9)

Besides magnetic films, lithographically made nanodots are a main topic in this thesis. To describe the shape anisotropy of nanodots an expression for cylinders derived by Millev et al. [37] is used:

Kshape,dot = − 1 2µ0M 2 S 1 + 2 πκ − 3 2 1 √ 1 + κ2 · 2F1 5 2; 1 2; 2; κ2 1 + κ2 !! (2.10)

κ = d/t is the the aspect ratio between the diameter d of the cylinder and the thickness t of the magnetic layer.2F1 is the Gaussian hypergeometric function.

When performing nanostructuring of a magnetic film into a nanodot the shape anisotropy changes by a value of ∆ Kshape = Kshape,dot− Kshape,film.

Magnetic anisotropy

In a solid certain directions of the magnetisation are preferred, called easy axes of magnetisation. Energetically unfavourable directions are called hard axes of magnetisation. The magnetic anisotropy is defined as the difference in energy density between the easy axis and the hard axis of magnetisation. This anisotropy is caused by a multitude of physical effects, the main contributions being the magneto-crystalline anisotropy, interface anisotropy and strain anisotropy.

Magneto-crystalline anisotropy

The magneto-crystalline anisotropy is caused by the spin-orbit interaction that couples the magnetic moments of the atoms to the crystal lattice of the solid. The easy axes of magnetisation are equal to certain crystal axes, depending on the crystal lattice. For hcp Cobalt the easy axis is the 001-direction of the lattice. Such a system with one preferred direction is called a uniaxial anisotropy and is described by

Euni/V = K1sin2(θ) + K2sin4(θ) + O

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2.2 Magnetic energy terms

K1 and K2 are the anisotropy constants in first and second order, V is the volume

of the system and θ is the angle between the easy axis and the magnetisation. In cubic crystals another anisotropy occurs, the cubic anisotropy. The energy density can be expressed by using the direction cosines of the magnetisation α1,α2

and α3. The energy density is given by:

Ecubic/V = Kcub,1 α2₁α2₂+ α2₂α2₃ + α2₂α2₃+ Kcub,2α21α 2 2α 2 3 (2.12)

Kcub,1 and Kcub,2 are the cubic anisotropy constant of the first and second order.

Higher orders are neglected.

Interface anisotropy

On surfaces or interfaces of thin films the translation symmetry is broken. This leads to another contribution of the anisotropy, which causes an easy axis of magnetisation perpendicular to the film plane. This interface or surface anisotropy is described by:

ES/V =

2KInt

t sin

2_(θ) _(2.13)

t is the thickness of the film and the factor 2 stems from the fact, that there are usually two interfaces. EInt decreases with higher film thickness and plays an

important part for the magnetism in thin films.

Magneto-elastic energy

In this chapter the magneto-elastic energy is discussed. Any elongation or com-pression of a crystal results in a change of the magnetisation, because the latter is connected to the crystal by spin-orbit coupling. This results in another anisotropy term, known as strain anisotropy. The magneto-elastic energy has been exten-sively studied by Sander et al. [38–41]. Though Co can grow in hcp as well as fcc structure, only the magneto-elastic energy of fcc Co is important in this thesis. The energy density is given by Kittel [42] or Lee [43]:

EME,fcc/V = B1

1α21+ 2α22 + 3α23

+ B2(4α2α3+ 5α3α1+ 6α1α2) (2.14)

i is the elastic strain tensor, Bi are the magneto-elastic coupling constants and

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order. Higher orders are discussed by Becker and Döring [44] and Carr [45], but are neglected in this thesis. The magneto-elastic coupling constants are given by:

B1 = −

3

2(c11− c12) λ100 (2.15)

B2 = −3c44λ111 (2.16)

cij are the elastic stiffness constants and λ the magneto-strictive strain constants.

The numbers of the constants are tabulated in [40] by Sander. It follows for fcc Co: c11= 242 GPa, c12 = 160 GPa, c44= 128 GPa, λ100 = 75 · 10−6, λ111 = −20 · 10−6,

B1 = −9.2 MJ/m3 and B2 = 7.7 MJ/m3. The magnetic anisotropy is defined as

the difference in energy density between the easy axis of magnetisation and the hard axis. For the films investigated in this thesis, this is the difference between a magnetisation pointing in the film plane and pointing parallel to the film normal. For a fcc crystal with a (111) texture this results in:

KME = B2(ip− oop) (2.17)

ip is the in plane strain and oop the out of plane strain. They are connected by

the elastic stiffness constants. Sander [40] gives the following relation:

oop = −

c11+ 2c12− c44

c11+ 2c11+ 4c11

2ip (2.18)

This results in oop = −0.57ip, hence:

KME = B2 · 1.57 ip (2.19)

Effective anisotropy

The above mentioned anisotropy terms can be summed up to an effective anisotropy:

KEff = KMC+ KShape+

2 KInt

t + KME = KV,eff + 2 KInt

t (2.20)

Depending on the film thickness the effective anisotropy might lie in the plane of the film (in-plane anisotropy) or perpendicular to the film plane (out-of-plane anisotropy). Usually, a negative sign is given to the in-plane contribution of the

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2.3 Single domain systems

anisotropy and a positive sign to the out-of-plane contribution. The transition from out-of-plane to in-plane anisotropy is called spin reorientation transition (SRT). KMC and KME can be understood as the volume anisotropy KV = KMC+ KME.

Volume anisotropy and shape anisotropy give the effective volume anisotropy KV,eff = KV+ Kshape.

2.3 Single domain systems

Two effects act on the magnetic moments in a solid. The exchange interaction favours the magnetic moments to align parallel to another. However, the demag-netisation energy favours an anti-parallel alignment, which minimises the stray field. The interplay of both effect results in the emergence of domains. That are regions within the solid, where the magnetic moments are aligned parallel. The domains themselves are not parallel to another. Typical domain state struc-tures are stripe domain or Landau domain strucstruc-tures. The transition region between two domains is called domain wall. The width of the domain walls is determined by the exchange interaction and the magnetic anisotropy. The exchange favours only a small rotation of each individual magnetic moment, to hinder a strong deviation from the parallel alignment. The anisotropy favours a large rotation in the hard axis of magnetisation. For a Bloch wall the width is given by δ0(Keff) = π

q

Aex

Keff [46]. Aex = 31.4 pJ/m

3 _{is the exchange constant}

of Co. Depending on the anisotropy one can find typical domain wall width of δ0(100 kJ/m3) = 56 nm and δ0(300 kJ/m3) = 32 nm.

Reducing the size of a magnetic structure will at a certain point result in a single domain state. It is then energetically unfavourable to create domains. Depend-ing on the size of the structure, different types of magnetisation reversal exist. For this thesis most important is the model of coherent rotation, also known as Stoner-Wohlfarth model. Magnetisation reversal by coherent rotation means, that all magnetic moments of the structure rotate uniformly from one state to the other like a single macrospin. Increasing the size of the structure will lead to another form of magnetisation reversal called domain wall nucleation. In this case a domain in the opposite magnetisation state will be created and grow in size until the whole structure has changed its state. The critical diamater for coherent rotation in a cylindrical nanostructure has been given by Skomski [47]

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as D(t) ≈ 23l20

t. The variable t defines the thickness of the magnetic material.

l0 =

r

2Aex

µ0M_S2 = 4.8 nm [46] is the magnetostatic exchange interaction length, with

MS(0 K) = 1.458 MA/m [48] as the saturation magnetisation. Typical diameters

are D(0.7 nm) = 757 nm and D(1 nm) = 529 nm. The nanostructures that are in-vestigated are between 16 nm and 45 nm in diameter. Therefore, coherent rotation is expected, which will be discussed in the next section.

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2.3.1 Stoner-Wohlfarth model

0 4 5 9 0 1 3 5 1 8 0 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 s in ² ( θ ) − 2 h c o s ( θ− φ ) Q ( ° ) 2 h = 0 2 h = 0 . 2 2 h = 0 . 4 2 h = 0 . 6 2 h = 0 . 8 2 h = 1 a ) _φ= 0 ° 0 4 5 9 0 1 3 5 1 8 0 0 . 0 0 . 5 1 . 0 1 . 5 s in ² ( θ ) − 2 h c o s ( θ− φ ) Q ( ° ) 2 h = 0 2 h = 0 . 2 2 h = 0 . 4 2 h = 0 . 6 2 h = 0 . 8 2 h = 1 b ) _φ= 9 0 ° - 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 7 5 ° 9 0 ° 4 5 ° 1 5 ° M /M S h 0 ° c ) - 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 Mz /M S 7 5 ° 8 9 ° 4 5 ° h 1 5 ° 0 ° d )

Figure 2.1: a) shows the uniaxial energy potential with a magnetic field applied in the

easy axis of magnetisation. h is the reduced field H/HK. The different colors represent

the different field strength. For h = 0 two minima can be seen, that represent the two states of magnetisation. They are separated by the energy barrier. When a magnetic field is applied the energy potential is altered. When the minimum disappears, the magnetisation is reversed.

b) shows the case when the magnetic field is applied in the hard axis of magnetisation. With increasing field, the energy barrier shrinks and the minima converge to another. Eventually only one minimum remains.

c) shows the hysteresis curves of the magnetisation M/M_Sin dependence of h for varying angles φ. At φ = 0◦ a rectangular hysteresis curve emerges. Moving closer to 90◦ will result in a closing of the hysteresis.

d) shows the perpendicular projection of the magnetisation M_z/MS. At 0◦ the hysteresis

curve is rectangular and gets consequently rounder in shape, when moving to 90◦. The two plateaus are the two states of magnetisation. When the switching field HSw is

reached, the magnetisation is reversed, which is seen as a jump in the hysteresis. The switching field is dependent of φ.

The model of coherent rotation was developed by Stoner and Wohlfarth and published in 1948 [49] and republished in 1991 [50]. A review is found in [51]. The

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model is based on an uniaxial anisotropy potential, that is effected by an external magnetic field, which is described by a Zeemann-term. The energy density is given by:

ESW/V = K sin2(θ) − µ0H MS cos (θ − φ) (2.21)

φ describes the angle between the easy axis of magnetisation and the external magnetic field. Of particular interest are the cases of the applied magnetic field parallel to the easy axis of magnetisation (φ = 0◦, see fig.2.21a)) and perpendicular to the easy axis (φ = 90◦, see fig.2.21b)). The magnetic field is displayed as the reduced field h = H/HK. The latter is the critical field, which is given by

HK= _µ2K₀_M

S.

In the first case, the deformation of the energy landscape with increasing magnetic field, will manifest in the vanishing of one of the minima and the state parallel to the magnetic field will be preferred. In the second case the energy barrier between the two minima will shrink and the two minima will converge until at a certain field, the energy barrier disappears and only one minimum remains. The energy barrier is defined as the product of anisotropy and volume of the structure: ∆E = KV . It is dependent on the magnetic field and is given by:

∆E = KV 1 − H HK n(φ) (2.22)

Pfeiffer [52] gave an approximation of the exponent, which is n(φ) = 0.86 + 1.14 · HSw(φ). In the easy and hard axis of magnetisation n = 2.

In the experiment, usually magnetic field sweeps are performed. Fig.2.21c) shows the magnetisation M/MS in dependence of the reduced field. These curves

are called hysteresis curves. Different angles φ are displayed. At φ = 0◦ the curve has a rectangular form. Moving to φ = 90◦, the hysteresis begins to close. The coercive field at φ = 0◦ and 90◦ is identical to the critical field HK.

The measurement technique, that is used in this thesis, is only sensitive to the perpendicular component of the magnetisation Mz. Fig.2.21d) shows hysteresis

curves of Mz/MS(h). The hysteresis does not close, when approaching φ = 90◦,

but becomes circular. The two plateaus seen in the graph are the two states of magnetisation. Once the magnetic field strength reaches the switching field HSw,

the magnetisation is reversed. The magnetisation reversal is represented by a jump in the hysteresis curve. The switching field HSw(φ) is depending on the

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angle between the magnetic field and the easy axis of magnetisation.

The angular dependence of the switching field is determined by deriving the local minimum of the energy landscape in dependence of θ and is given by:

HSw(θ) = 2 K µ0MS sin23 (θ) + cos 2 3 (θ) −3₂ (2.23)

HSw/HK(φ) is plotted in fig.2.2a). The black line shows the angular dependence

of the switching field given by the Stoner-Wohlfarth model. The switching field is at maximum in the easy axis (φ = 0◦) and the hard axis of magnetisation (90◦ and −90◦_{). The curve is symmetric to 45}◦ _{and −45}◦_{, where there is a minimum. The}

red line shows an extension of the model, that was proposed by Kronmüller [53]. The extension adds the second order of the anisotropy K2 and is given by:

HSw,Kronm. = HSw  1 + 2K2 K1 (− tan(φ))23 1 + (− tan(φ))23   (2.24)

The equation is valid for K2/K1  1. In the plot a ratio K2/K1 = 0.25 is

chosen, that is in alignment to the experiment. The second order of the anisotropy increases the switching field in the hard axis of magnetisation. The easy axis remains unchanged and the local minima stay at 45◦. Chang [54] also investigated the second order and gave an analytical solution. His findings in the case of K1 > 0 and K2 > 0 and K2/K1 1 are in close resemblance to the solution

given by Kronmüller [29]. Another way of displaying the angular dependence of the switching field is the Stoner-Wohlfarth astroid, where the switching field is separated into the perpendicular and parallel contribution (see fig.2.2b)). In order to understand the three dimensional angular dependence of HSw, the astroid can

be rotated around the ordinate. The two dimensional astroid can be understood as a slice, that is cut out of the three dimensional surface. Fig.2.3 shows the three dimensional switching surface of the Stoner-Wohlfarth model. The switching surface is defined by certain characteristics. There is a distinct easy axis point, that is expressed by a sharp peak in the direction of the easy axis of magnetisation. The hard plane of magnetisation has a circular shape.

The angular dependence of the switching field is good indicator for the reversal mode of the investigated nanostructure. Next to coherent rotation, also domain wall nucleation is possible in single domain systems, which leads to a different

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angular dependence. This will be briefly explained in the next section. - 9 0 - 4 5 0 4 5 9 0 0 . 5 1 . 0 1 . 5 HS w /H K f ( ° ) H S w , S W/ H K H S w , K r o n m ./ HK a ) K ₂ / K ₁= 0 . 2 5 - 1 0 1 - 1 0 1 HS w , ⊥ /H K H _{S w , | |}/ H _K S t o n e r - W o h l f . a s t r o i d K r o n m ü l l e r a s t r o i d b ) K ₂/ K ₁= 0 . 2 5

Figure 2.2: a) The plot displays the angular dependence of the switching field. The

black line shows the Stoner-Wohlfarth model. HSw peaks in the easy and hard axis of

magnetisation and is axis symmetric. Also there is a symmetry around 45◦. The red line represents an extension of the model made by Kronmüller, that takes the second order of the anisotropy into account. This results in an increase of hSw in the hard axis.

b) is an alternative form of presentation, that is called the Stoner-Wohlfarth astroid.

HSw is separated into the perpendicular and parallel contributions. The red line shows

again the extension of Kronmüller. The astroid can be understood as a slice of the three dimensional switching surface. The latter can be created by rotating the astroid around the ordinate.

Figure 2.3: The three dimensional switching surface of the Stoner-Wohlfarth model

is presented. On the left side, a viewpoint from the side is shown. The surface has a distinct easy axis point. On the right side, a viewpoint from the top is seen. The hard plane of magnetisation has a circular shape.

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2.4 Thermal effects

2.3.2 Domain wall nucleation

The model to describe domain wall nucleation in a single domain nanostructure was published by Kondorsky in 1940 [55]. In this case, the magnetic moments will not rotate like a macrospin. Instead a nucleus of the reversed magnetisation state will form somewhere in the nanostructure. This reversed domain will grow and the domain wall will move through the sample until the whole magnetisation is reversed. Due to the time scale of the process, in experiment domain wall nucleation can not be distinguished from coherent rotation by looking at the hysteresis curve. Instead one can measure the angular dependence of the switching field. While for coherent rotation the angular dependence is given by eq. 2.23. For domain wall nucleation the angular dependence is proportional to 1/ cos(θ).

2.4 Thermal effects

In single domain structures an effect called superparamagnetism emerges above a certain temperature. The temperature is called blocking temperature TB. Once

the thermal energy kBT becomes comparable in size to the energy barrier KV

spontaneous magnetisation reversal will occur. A common definition for the blocking temperature is given by KV = 25kBT . Superparamagnetism displays the

same characteristics as paramagnetism, albeit with a much higher magnetisation. The average time between two magnetisation reversals, called switching frequency, is given by the following equation, which was developed by Néel based on an Arrhenius ansatz and is therefore known as Néel-Arrhenius law [56]

f = f0exp(−

KV kBT

) (2.25)

f0 is the exponential prefactor. After Néel, Brown took on the problem and

found a solution based on the magnetisation dynamics [57,58]. The magnetisation dynamics is described by the Landau-Lifschitz-Gilbert equation (LLG). Using the LLG as a basis, Brown derived the switching frequency, which is always given by the form of f = f0exp(−_k∆E

BT). Hence the equation is also known as Néel-Brown

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along the easy axis of magnetisation the following rate equation is derived: f±= f0,±exp − ∆E kBT ! = f0,±exp −KV kBT (1 ± h)2 (2.26)

’+’ describes the change of magnetisation orientation from the energetically preferred minimum into the metastable minimum, while ’−’ describes the opposite case. The attempt frequency f0,±(h, T ) is given by Brown as:

f0,±(h, T ) = αγ 1 + α2 · v u u t(µ0HK) 2 MSV 2πkBT · (1 ± h) · (1 − h)2 _(2.27)

γ is the gyromagnetic ratio, α is the damping parameter of the material and HK is the anisotropy field, which is given by HK = _µ2K₀_M

S. Usual values of the

attempt frequency f0 are in the range of 109Hz and 1011Hz. The pre-factor plays

a prominent role in this thesis and will be discussed later on in the experimental section.

Spontaneous magnetisation behaviour with an applied magnetic field

Coffey and Kalmykov [59] calculated the effect of an applied magnetic field on the attempt frequency f0 = 1/τ0. The magnetic field is applied in the hard axis

of magnetisation. They looked at two specific cases, that depend on the damping parameter α. The two cases are called very low damping (VLD) for α 1 and intermediate high damping (IHD) for α > 1. For the VLD case the following equation is found, where σ = KV

kBT and h = H/HK β = V kBT. 1/fVLD(h, T ) = π ·h1 −13 6h + 11 8h 2₋ 3 16h 3_{+ O (h}4₎i 8σ2_·q_{h (1 − h)}2 expσ (1 − h)2 (2.28) With τN = M_kSV BT · (1+α2₎

2γα , the IHD case is given by:

1/fIHD(h, T ) = 2τNπ √ h σ√1 + h · (1 − 2h +q1 + 4h(1 − h)α−2₎exp σ (1 − h)2 (2.29) The exponential term of both functions is identical to the Néel-Arrhenius law. The frontal terms can be understood as field dependent attempt frequencies f0,VLD(h)

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2.5 Magnetotransport effects

and f0,IHD(h).

Temperature dependence of the switching field

Below TB, thermal energy also effects the switching field of single domain structures.

The magnetisation may be reversed before the local minimum in the energy potential disappears, due to thermal activation. The switching field is thus smaller than in the case of the Stoner-Wohlfarth model. Different models for HSw(T ) have

been compared by Neumann [29]. He finds that the solution given by Garg [60] describes the switching field best:

HSw(T ) = 2K µ0MS  1 −  1 + γEM 2 lnkBT f0 µ0MSV 1 R   v u u t kBT KV ln kBT f0 µ0MSV 1 R !  (2.30)

γEM = 0.5772 is the Euler-Mascheroni constant. R is the sweeping rate of the

magnetic field. In the experiment usually 0.01 T/s is used.

2.5 Magnetotransport effects

In general, electric resistivity is described by Ohm’s law, which connects the current density ~j and the electric field ~E by the electrical conductivity tensor ¯σ.

~j = ¯σ · ~E (2.31)

The inverse of the conductivity tensor is the resistivity tensor ¯ρ = ¯σ−1. In a classical sense, Ohm’s law can be derived by the Drude model. In the Drude model, the metal consists of positively charged ions while the electrons are treated like a classic gas. The electrons, that move with a constant velocity, are permanently colliding with the ions, with an average collision time τ . The conductivity, that is a scalar in the model, is given by σ = e_m2nτ

e . n is the electron density and me the

electron mass.

Non-classical Ohm’s law can be derived by solving the Boltzmann equation. The mean collision time τcol is given by τcol = λ/vF. The latter is the Fermi velocity

vF =

q

2EF/me, where EF is the Fermie energy. λ is the mean free path, which is

typically 10 − 100 nm at room temperature.

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interfaces, as well as phonons, and magnons. As the electron-phonon as well as the electron-magnon scattering is temperature dependent, so is τ . The different processes are connected by Matthiesens’s rule, which is given by:

1 τcol = 1 τdefects + 1 τint + 1 τph(T ) + 1 τmagn(T ) (2.32)

Usually, only scattering on lattice defects and phonons are take into consideration. Scattering at interfaces is only important in ultrathin films and the contribution of electron-magnon scattering is small compared to electron-phonon scattering. The temperature dependence of the specific resistivity is decided by the tem-perature dependence of the electron-phonon scattering, which is given by the Bloch-Grüneisen formula: ρ = ρ0 + ρ(T ) = ρ0+ A _T ΘD Z ΘD/T 0 x5dx (ex_{− 1)(1 − e}−x₎ (2.33)

A is a material constant and ΘD is the Debye temperature.

2.5.1 Longitudinal magnetoresistance effects

A magnetic field applied to an electrical conductor will lead to a change in resistivity of the conductor, which is known as magnetotransport. In a ferromagnet, like the Pt/Co/Pt samples investigated in this thesis, additionally to the magnetic field ~H the magnetisation ~M has to be considered, thus leading to a resistivity tensor ¯ρ( ~H, ~M ). The latter is connected to the electrical field ~E and the electrical current ~j by Ohm’s law:

~

E = ¯ρ( ~H, ~M ) · ~j (2.34)

In this thesis the current is applied in the xy-plane of the film, which leaves two resistivity contributions ρx and ρy. The former is the longitudinal resistivity (the

resistance along the current direction ~j) and the latter is the transversal resistivity (the resistance perpendicular to the current direction).

The longitudinal magnetoresistance effects are defined by Onsager’s law as even functions of the resistivity: ρx( ~H, ~M) = ρx( ~−H, ~−M ). In this thesis the

follow-ing magnetoresistance (MR) effects are discussed: Anisotropic MR, anisotropic interface MR, geometrical size effect, Lorentz MR and Spin disorder MR

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Anisotropic magnetoresistance

The anisotropic magnetoresistance (AMR) occurs in ferromagnetic materials and was discovered by W. Thompson in 1856 [61]. As a consequence of the AMR, the resistance is depending on the angle Φ between magnetisation and the applied electric current Φ]( ~M ,~j). Models describing the AMR are based on an anisotropy in the spin orbit interaction [62–65]. Usually, the resistivity is larger in the longitudinal case of ρlong with Φ = 0◦ than for the transversal

case of ρtrans with Φ = 90◦. The magnitude of the AMR is usually definded by

∆ρAMR = ρlong − ρtrans > 0. In the case of technical saturation M = MS, the

angular dependence of the AMR is given by

ρ(Φ) = ρtrans+ ∆ρAMR cos2(Φ) (2.35)

Kobs and Oepen [66] showed that the AMR in Co/Pt multilayers depends on the thickness of the Co layer, because of an additional AMR contribution that stems from the interfaces. The overall magnitude of the AMR is thus determined by the ratio of interface to bulk.

Anisotropic interface magnetoresistance and geometrical size effect

In 2010 Kobs et al. [67] found a new effect in ultrathin multilayers, which was called anisotropic interface magneto resistance (AIMR). This effect behaves similar to the AMR though it depends on the angle between magnetisation and film normal Θ]( ~M , ~n). The magnitude of the AIMR is given by the difference between the polar case ρ(Θ = 0◦) = ρpolar and the transversal case ρ(Θ = 90◦) = ρtrans,

hence ∆ρAIMR = ρpolar− ρtrans. In textured films, the angle dependence is nearly

identical to the AMR albeit higher orders can be observed especially for Co/Ni multilayers and to a lesser extent in Co/Pt multilayers:

ρ = ρtrans+ ∆ρAIMR(cos2(Θ) + cos4(Θ) + cos6(Θ)) (2.36)

Phenomenology the effect can be explained with magnetisation-dependent scat-tering probabilities of the electrons on interfaces [66]. Weinberger developed a fully relativistic model, that includes spin-orbit interaction. The AIMR is only detectable in thin films, where the magnetic layer is less then 50 nm [68].

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The geometrical size effect (GSE) was discovered in 2005 by Gil et al. [69]. The GSE stems from magnetisation dependent scattering probability in respect to the texture of the film. In Pt/Co/Pt film systems the GSE occurs in the same geometry as the AIMR and is thus superimposed with the latter. It has a negative sign and, because it is a bulk effect, is independent of the thickness. Therefore the GSE serves as a constant negative offset to the AIMR in Co/Pt films [67].

Lorentz magnetoresistance

The Lorentz magneto-resistance (LMR) is an anisotropic effect that manifest as an increase of the resistivity above technical saturation, where the magnetisation is aligned parallel to the magnetic field. The LMR is a result of the Lorentz force. An external magnetic field that is applied transversal to the current direction forces the electrons on helical orbits, which reduces the effective mean free path in the current direction. The strength of the LMR goes quadratic with the applied magnetic field [70]:

ρLMR ∝ B2 (2.37)

The LMR also occurs when the magnetic field is applied in the direction of the electric current, though the magnitude of the effect is smaller [71].

Spin-disorder magnetoresistance

The saturation magnetisation MS is temperature dependent, which will become

an important aspect in later parts of this thesis. At higher temperatures the temperature dependence can be described by Bloch’s T3/2 _{law [}₇₂_]:

MS(T ) = MS(0 K)(1 − bT3/2) (2.38)

b is the Bloch constant, which is a constant, that depends on the exchange stiffness A and the lattice constant a of the material. Stearns gives b = 1.5 · 10−6K−3/2 [73] for hcp Co above 100 K. Whereas Liu et. al give b = 3.3 · 10−6K−3/2 [74] for bulk Co. In Co nanoparticles or nanostructures [75–77] the Bloch constant might deviate from this values, because of surface effects. This might lead to a higher temperature dependence of the saturation magnetisation.

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reduction of magnon density leads to a decrease in magnon-electron scattering, whereby the resistance will decrease. This effect is known as spin-disorder magneto resistance (SMR). The SMR is an isotropic effect that exhibits a linear dependence of the resistance in respect to the magnetic field [78]:

ρLMR ∝ − |B| (2.39)

At very low temperatures the SMR deviates from the linear behaviour. A change in sign is observed and the resistance is increasing with the field [79]. Though this could also be the result of the LMR, when all magnons are annihilated and magnon-electron scattering (and thus the SMR) completely vanishes.

2.5.2 Transversal magnetoresistance effect

Normal and anomalous Hall effect

When a magnetic field µ0HZ is applied perpendicular to an electric current a

voltage will emerge, that is perpendicular to the field and the current. This effect was discovered in 1879 by Edwin Hall and named Hall effect [80,81]. The Hall effect is caused by the Lorentz force, which deflects the conducting electrons perpendicular to the field and current direction jX. The emerging voltage is known

as Hall voltage UHall and is described by:

UHall = RNHE

IXµ0HZ

t (2.40)

tis the thickness of the material and RNHEis the Hall constant, which is a material

parameter.

In 1880 Hall discovered the anomalous Hall effect [82,83], that emerges only in ferromagnetic material, which possess a spontaneous Magnetisation MS, e.g. Fe,

Co and Ni. This effect is caused by Spin-Orbit interaction, which results in spin dependent scattering probabilities. Phenomenologically, normal and anomalous Hall effect are described by:

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RAHEis the anomalous Hall constant. The anomalous Hall effect is often by orders

of magnitude higher than the normal Hall effect. For the materials used in this thesis, cobalt and platinum, the following values are found in literature. The normal Hall constant in cobalt and platinum are RNHE,Co = −1.1 · 10−10m3/C

and RNHE,Pt = −2, 3 · 10−11m3/C, while the anomalous Hall constant of Co is

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3 Sample preparation and experimental

details

In this chapter the sample preparation and experimental details are discussed. The main emphasis will lie on the Pt/Co/Pt system that is investigated in this thesis. Also the lithography and nano-structuring that was performed to create the Hall bars and nanodots will be explained. An expansion of the measurement principle will be shown with the idea to measure magneto-resistance effects in nanodots. Furthermore different nanodot lattices will be shown, that were created for investigations with synchrotron radiation.

3.1 Pt/Co/Pt sample system

In this thesis measurements of ultra-thin Pt/Co/Pt films and nanostructures have been performed. The films have been investigated in the group of Prof. Oepen over the past two decades [21–27]. The samples are created by electron cycle resonance (ECR) sputtering and direct current (DC) magnetron sputtering. Starting with a SiO2 or Si3N4 substrate a Pt seed layer is evaporated by ECR sputtering, which

induces a good texture. Afterwards another layer of Pt is evaporated by DC magnetron sputtering. This is followed by the Co layer and a Pt cap layer, both of them also made by DC magnetron sputtering. The two interfaces between the Co and Pt layers ensure a strong uniaxial anisotropy, that is perpendicular to the film plane for thin Co layers. Typical layer thicknesses are (4 + 1) nm or (4 + 3) nm for the Pt seed layer and 3 nm for the Pt cap layer. The Co thickness is varied from 0.7 nm to 30 nm, whereby the system will undergo a spin reorientation transition between 1.2 nm and 1.5 nm, depending on the substrate.

Prior investigations [26,27] insist that the Co layer will grow in a fcc-structure and is strained at thin Co thickness, because of different lattice parameters of Pt and

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Figure 3.1: (a) and (b) depict a model of the film system. The film is evaporated on

a Si3N4 or SiO2 substrate. The first layer consists of 4 nm of Pt that is deposited by

electron cyclotron resonance sputtering. This layer of Pt is characterised by a very good texture. On top of the Pt another layer of 1 − 3 nm of Pt is deposited by direct current magnetron sputtering. This Pt layer is deposited with less energy, so that the thickness of the interface with the following Co layer is minimised. The Co layer is varied between 0.7 nm and 30 nm, depending on the experiment. Out-of-plane anisotropies are achieved below 1.2 nm and everything above will have an in-plane anisotropy. Above the Co layer another 3 nm of Pt is deposited by DC magnetron deposition. This layer creates another interface to enhance the out-of-plane anisotropy and also protects the Co layer from oxidation.

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3.2 Measurement technique

Co. The strain contributes to the out-of-plane contribution of the anisotropy. Also the samples are poly-crystalline, with a typical grain diameter of about 16 nm [31]. These grains are tilted to the film normal. The tilt can be described by a Gaussian distribution with a peak in the direction of the film normal at 0◦. The half width maximum is 11◦ and the maximal tilt is 23◦. The tilt is isotropically distributed in all spatial directions and therefore disappears on average. The ramifications of these structual properties will be discussed in the main part of this thesis.

3.2 Measurement technique

The goal of this thesis was to study the magnetic properties of ultrathin Pt/Co/Pt films and nanostructures, with the main focus on the magnetic anisotropy. The measurement principle for the films is basic magnetotransport measurement, with a direct current applied. Pads made of gold are used to contact the samples by wire bonding and the longitudinal as well as the transversal voltage are measured. The nanostructures are probed by Hall magnetometry. Therefore nanosized Hall bars are used to study the magnetisation behaviour of single nanodots. The basic effects behind the method are the ordinary and anomalous Hall effect. The ordinary Hall effect (OHE) occurs in Pt and Co and is proportional to the applied magnetic Field. The anomalous Hall effect (AHE) emerges only in Co, as it solely appears in ferromagnetic materials. It is dependent of the magnetisation. The resulting Hall voltage is given by:

UHall= µ0(ROHEHZ+ RAHEMZ) IX/t (3.1)

ROHE and RAHE are the corresponding Hall constants and HZ and MZ the

perpen-dicular components of the applied field and the magnetisation of the sample. IX

is the applied current and t the dimension of the sample. Both effects are present in Pt/Co/Pt systems, but the AHE term RAHEMZ dominates the OHE term by

orders of magnitude. Thus the perpendicular component of the magnetisation is directly proportional to the Hall voltage UHall. Since the investigated samples

possess an easy axis of magnetisation that lies perpendicular to the film plane, the magnetisation is directly measurable.

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3.3 Lithography and nano-structuring

Figure 3.2: a) A microscope image of the four gold plates to contact the samples. The

area between the pads has a size of 20 µm x 20 µm. b) A SEM micrograph of a typical Hall bar. The leads have a width of 80 nm and the nanodot has a diameter of 45 nm.

3.3 Lithography and nano-structuring

The creation of the nanostructures requires distinguished fabrication processes that are based on photo- and electron-beam-lithography [29,30]. In a first step, the Pt/Co/Pt film is covered with contact pads made of gold. This is done with standard photo-lithography technique utilising a shadow mask and a negative photo-resist. Afterwards Au is evaporated by sputter coating and the remaining resist is removed in an ultrasonic bath. These golden contact pads are used for aluminium wire bondingto contact the sample. The gold pads are shown in fig.3.2a) and a finished Hall bar in fig.3.2b).

Afterwards an array of nanodots is fabricated between the four contact pads. The process is depicted in fig.3.3. This is done by using electron beam lithography and a negative electron beam resist to create cylindrical shadow masks. With the SEM and commercially available electron beam resist, a minimal diameter of 35 nm was possible. To further reduce the diameter of the shadow masks an oxygen plasma could be used used. Unfortunately the cylindrical shadow mask would fall over, if the ratio of diameter and height (80 nm) would become critical. Due to this the resist was diluted and the height of the resist reduced. This allowed to create shadow masks with a diameter as small as 12 nm. Afterwards the film is etched by using argon ion milling. The cylindrical shadow masks protect the film beneath them, so that the dots are carved into the film. The etching process is stopped in

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Figure 3.3: The figure shows the creation of the nanodots from a thin film. (a) The

starting point is a thin film, that was created by sputter deposition. The composition of the film is described in fig.3.1. The procedure is optimised for this film composition but can also be applied to other systems. (b) The film is coated with a negative electron beam resist by using spin coating. (c) The resist is exposed to the electron beam. An array of dots is written. (d) The resist is developed. The parts of the resist, that were not exposed to the electron beam are removed by the developer. An array of resist cylinders remains, that serve as a shadow mask. (e) The film with the shadow mask on top is subjected to an ion milling process. The film is removed, except for the parts that are protected by the shadow mask. The ion milling is stopped in the lower Pt layer and the sample is cleaned to remove the remaining resist.

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Figure 3.4: The figure shows the creation of the Hall bar. (a) The sample from fig.3.3e)

serves as the starting point. (b) The sample is coated with a negative electron beam resist. (c) The resist is exposed to the electron beam. A cross is written by the electron beam. (d) The resist is developed and the non-exposed resist is removed. The cross shape remains on the sample and serves as a shadow mask. (e) The remaining film is removed by ion milling. The part beneath the shadow mask is protected from the ion milling. (f) The sample is cleaned and the remaining resist is removed. A Hall bar is created from the remaining Pt layer, with a single nanodot in the crossing area of the Hall bar.

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the Pt seed layer, which will later be used as the current lead through the nanodot. Usually about 2 nm of the seed layer are removed. After ion milling the diameter of the nanodots will always exceed that of the shadow masks. Possible reasons for this are redeposition of sputtered materials or a bloating of the shadow mask during the ion milling process. Nanodots with a diameter ranging from 16 nm to 45 nm were fabricated and investigated in this thesis.

Finally the process is repeated to create the nanosized Hall bar, that served as the aforementioned current lead and the measuring probe for the magnetisation. This can be seen in fig.3.4. Again using electron beam lithography and utilising the alignment program of the software, a Hall bar shadow mask is build above the nanodot array. The width of the single leads is usually chosen to be 80 nm though it may also be smaller, e.g. 60 nm, depending on the size of the nanodot. With perfect alignment the crossing area will cover a single nanodot. Afterwards the ion milling is used once again, this time removing the remaining seed layer, except where it is protected by the shadow mask. The latter now needs to be removed, which is usually achieved by oxygen plasma, though sometimes a treatment with peroxymonosulfuric acid is necessary. Usually 36 samples are produced on one substrate, with at least half of them defective, as the alignment of nanodots and Hall bar did not work out or for other reasons like a defect in the resist.

The typical layout is the Hall bar shown fig.3.2 with the four leads. Two of the leads will be used to apply the current. Usually 20 − 40 µa are applied. The other two leads will be used to measure the Hall voltage. The voltage usually has a magnitude of several hundred nV. Since it was interesting to also measure longitudinal magnetoresistance effects, the layout was extended. To achieve this, eight contact pads were put on the sample and the Hall bar had two additional leads, to pick up the longitudinal voltage. This is shown in fig.3.5. These additional leads ought to be as close to the crossing area, that contains the nanodot, as possible. This was limited due to the proximity effect. The lead for the Hall voltage and the two leads for the longitudinal voltage would fuse together if the distance between them is to small. A distance of 60 nm could be achieved. While the lithography was successful, the longitudinal magnetoresistance of a single nanodot could not be probed. The reason for this is probably the poor filling factor. Due to this the magnetoresistance effects of the magnetic nanodot are superimposed by effects stemming from the Pt seed layer. As a consequence,

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Figure 3.5: a) Displays a microscope image of the eight gold plates to contact the

samples. The area between the pads has a size of 40 µm x 40 µm. b) Additional leads have been added to the Hall bar, allowing the measurement of the longitudinal voltage. c) The width of the leads is 80 nm. The space between the leads is 60 nm.

the idea to measure longitudinal magnetoresistance effects in single magnetic nanodots was no longer pursued.

In collaboration with projects working with synchrotron radiation big arrays of magnetic nanodots on ultrathin Si3Ni4 (t = 25 − 100 nm) membranes were made.

Fabricating these had a very particular difficulty, as the membranes would very easily rupture with the slightest bit of touch, thus requiring pronounced fine-motor skills. The two techniques based on synchrotron radiation used two investigate the nanodots were magnetic x-ray holography and coherent x-ray scattering. For x-ray holography dot arrays in simple cubic and kagome lattice were made with varying distance between the dots. Since more magnetic material is needed to do holography, Pt/Co/Pt-multilayers were used instead of single layers. In fig.3.6

an SEM image of a Kagome lattice is depicted as well as a magnetic hologram. The measurements were performed by J.Wagner, R.Frömter and others and are discussed in J.Wagners PhD thesis [85].

For the coherent x-ray scattering simple cubic lattices were made. One lattice was a chequerboard with alternating hard and soft magnetic nanodots. This was done by using positive electron beam resist. With electron beam lithography nanosized holes were created in the resist and later filled with magnetic material. Afterwards the resist was removed and magnetic nanodots remained. The process was repeated and with alignment technique it was possible to make this aforementioned

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Figure 3.6: a) Displays a Kagome lattice of multi-layered Co/Pt nanodots. The sample

was created on a silicon nitride membrane that allows X-ray transmission measurements. b) A magnetic X-ray holografie measurement of a Kagome lattice as shown in a). The 110 nm in the upper right describe the distance from center point to center point of to aligning dots. The measurement was performed by J. Wagner, R. Frömter and others at the Petra 3 beamline at Desy. The technique is described in Wagners PhD thesis [85].

chequerboards. In fig.3.7 SEM images of the chequerboard are shown.

3.4 Experimental setup

The samples are electrically contacted by using wire wedge-bonding. Various experimental setups were used over the course of the thesis. Mainly a setup consisting of a cooling finger and a rotatable electro-magnet has been used. The cooling finger allows to investigate the sample in a temperature range of 77.5 K and 300 K, when using liquid nitrogen. The electro-magnet can apply magnetic fields up to 800 mT. The electro-magnet can be rotated in one plane by 360◦, allowing measurements in the film plane, film normal and in arbitrary angles in between.

The second setup is a SpectroMag, which is a cryostat with a superconducting coil from Oxford Instruments. The SpectroMag is used in a temperature range of 2.5 K up to 300 K. Magnetic fields up to 6 T are applied. The sample holder can be rotated within the magnetic field. Using an in plane or out of plane holder allows to measure arbitrary angles.

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3.4 Experimental setup

Figure 3.7: (a) The first lattice of magnetically soft dots is created by using an additive

lithography technique. The diameter of the dots is 200 nm.(b) A positive electron beam resist is layerd on top of the dots. The black holes serve as evaporation mask for the second lattice. The two lattices are aligned by the software. (c) The second lattice of dots is created and fits shows a good alignment with the first lattice. (d) and (e) The finished checkerboard is shown in larger magnification. The lattice constant of the checkerboard is 500 nm. The overall size of the checkerboard is 80 µmx 80 µm

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Third, is the Dynacool a closed-cycle cryostat by ’Quantum Design’. The Dynacool can vary the temperature very fast in a range of 2.5 K up to 300 K. Like in the SpectroMag up to 6 T are applied, but only perpendicular to the sample.

The fourth experimental setup is a three dimensional vector magnet from ’Oxford Instruments’. This cryostat has three superconducting coils. Therefore the magnetic field can be applied in every spatial angle up to 500 mT.

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4 Magnetisation behaviour of ultrathin

magnetic films

4.1 Temperature dependence of the anisotropy in ultrathin

magnetic films

4.1.1 Introduction

Sec.3.1 introduced the Co/Pt multilayers that have been the subject of extensive research over the past two decades [21–27]. The Co/Pt films are always fabricated in the same way. Via electron cyclotron sputtering a Pt seed layer is deposited on either a silicon oxide (SiO2) or a silicon nitride (Si3N4) substrate. The high

energy of the deposited atoms creates a film with a fcc (111) texture. Afterwards another Pt layer, followed by the Co layer and a final Pt cap layer is deposited on the ECR-Pt seed layer. For this part DC-magnetron sputtering is used. The lower energy of the technique generates better defined interfaces. The Co layer grows in a (111) fcc crystal structure and the film is poly-crystalline. The typical grain size is 16 nm. The grains are also tilted from the film normal. The tilting can be described by a Gaussian distribution with the peak at zero degree. For a SiO2

substrate a sigma of σ = 11◦ and a maximal tilting of 23◦ are found. The tilting is isotropically distributed in all spatial directions. The magnetic properties of the film can be described by an uniaxial anisotropy model. Most importantly, the films exhibit a spin reorientation transition, meaning the easy axis of magnetisation switches from in-plane for a high Co thickness to out-of-plane for a small Co thickness. When the transition occurs depends on the substrate. Usually the SRT lies between 1.5 nm and 1.2 nm. The films are well understood, nevertheless open questions remain, for example the temperature dependence of the ferromagnetic anisotropy.

Comparison of the magnetic properties of ferromagnetic films and nanostructures